3146. Permutation Difference between Two Strings 

Description

You are given two strings s and t such that every character occurs at most once in s and t is a permutation of s.

The permutation difference between s and t is defined as the sum of the absolute difference between the index of the occurrence of each character in s and the index of the occurrence of the same character in t.

Return the permutation difference between s and t.

Example 1:

Input: s = "abc", t = "bac"

Output: 2

Explanation:

For s = "abc" and t = "bac", the permutation difference of s and t is equal to the sum of:

The absolute difference between the index of the occurrence of "a" in s and the index of the occurrence of "a" in t.
The absolute difference between the index of the occurrence of "b" in s and the index of the occurrence of "b" in t.
The absolute difference between the index of the occurrence of "c" in s and the index of the occurrence of "c" in t.

That is, the permutation difference between s and t is equal to |0 - 1| + |1 - 0| + |2 - 2| = 2.

Example 2:

Input: s = "abcde", t = "edbac"

Output: 12

Explanation: The permutation difference between s and t is equal to |0 - 3| + |1 - 2| + |2 - 4| + |3 - 1| + |4 - 0| = 12.

Constraints:

1 <= s.length <= 26
Each character occurs at most once in s.
t is a permutation of s.
s consists only of lowercase English letters.

Solutions

Solution 1: Hash Table or Array

We can use a hash table or an array of length $26$, denoted as $\textit{d}$, to store the positions of each character in the string $\textit{s}$.

Then, we traverse the string $\textit{t}$ and calculate the sum of the absolute differences between the positions of each character in the string $\textit{t}$ and the positions in the string $\textit{s}$.

The time complexity is $O(n)$, where $n$ is the length of the string $\textit{s}$. The space complexity is $O(|\Sigma|)$, where $\Sigma$ is the character set. Here, it is lowercase English letters, so $|\Sigma| \leq 26$.

Python3

class Solution:
    def findPermutationDifference(self, s: str, t: str) -> int:
        d = {c: i for i, c in enumerate(s)}
        return sum(abs(d[c] - i) for i, c in enumerate(t))

Java

class Solution {
    public int findPermutationDifference(String s, String t) {
        int[] d = new int[26];
        int n = s.length();
        for (int i = 0; i < n; ++i) {
            d[s.charAt(i) - 'a'] = i;
        }
        int ans = 0;
        for (int i = 0; i < n; ++i) {
            ans += Math.abs(d[t.charAt(i) - 'a'] - i);
        }
        return ans;
    }
}

C++

class Solution {
public:
    int findPermutationDifference(string s, string t) {
        int d[26]{};
        int n = s.size();
        for (int i = 0; i < n; ++i) {
            d[s[i] - 'a'] = i;
        }
        int ans = 0;
        for (int i = 0; i < n; ++i) {
            ans += abs(d[t[i] - 'a'] - i);
        }
        return ans;
    }
};

Go

func findPermutationDifference(s string, t string) (ans int) {
	d := [26]int{}
	for i, c := range s {
		d[c-'a'] = i
	}
	for i, c := range t {
		ans += max(d[c-'a']-i, i-d[c-'a'])
	}
	return
}

TypeScript

function findPermutationDifference(s: string, t: string): number {
    const d: number[] = Array(26).fill(0);
    const n = s.length;
    for (let i = 0; i < n; ++i) {
        d[s.charCodeAt(i) - 97] = i;
    }
    let ans = 0;
    for (let i = 0; i < n; ++i) {
        ans += Math.abs(d[t.charCodeAt(i) - 97] - i);
    }
    return ans;
}

C#

public class Solution {
    public int FindPermutationDifference(string s, string t) {
        int[] d = new int[26];
        int n = s.Length;
        for (int i = 0; i < n; ++i) {
            d[s[i] - 'a'] = i;
        }
        int ans = 0;
        for (int i = 0; i < n; ++i) {
            ans += Math.Abs(d[t[i] - 'a'] - i);
        }
        return ans;
    }
}